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Title	Name	Date
[QUE/TH-02001] TH-PROBLEM Consider a closed cylinder whose walls are adiabatic. The cylinder is divided into three equal parts $A_1$, $A_2$ and $A_3$ by means of partitions $S_1$ and $S_2$, which can move along the length of the cylinder without friction. The partition $S_1$ is adiabatic and $S_2$ is conducting. Initially, each of the three parts contain one mole of Helium gas, which can be treated as an ideal gas, is at pressure $P_0$, temperature $T_0$ and volume $V_0$. Assume the specific heat at constant volume $C_v\,=\,\frac{3R}{2}$ and the specific heat at constant pressure $C_p\,=\,\frac{5R}{2}$. Now, heat is supplied to the to the left most partition $A_1$ till the temperature in part $A_3$ becomes $T_3\,=\,\frac{9T_0}{4}$ Find the final volume, pressure and temperature in terms of $V_0$, $P_0$ and $T_0$. Assume the entire process is quasistatic. \vskip 3mm 3. ( Continuation of problem 2) (a) What is work done by the gas in $A_1$ ? (b) What is the heat supplied to the gas in $A_1$?	AK-47	22-01-14 10:01:44
[QUE/TH-05003] TH-PROBLEM Consider $n$ mole of ideal gas whose entropy is given by $$ \frac{n}{2}\left[c_1\,+\,5R{\ln}\frac{U}{n}\,+\,2R{\ln}\frac{V}{n} \right]$$ where $R$ is the univeral gas constant, $U$ the internal energy, $V$ the volume and $c_1$ a constant. Calculate the specific heats $c_V$ and $c_p$ A room is at a temperature $273^o$ K which is in equilbrium with the surroundings. One hour after turning on a heater, the room is at $300^o$ K. Assuming the air is described by the equation given above, find the energy density for the two different temperatures. Answer should be in terms of the atmospheric pressure $P_0$, assume it is constant and the room is always at $P_0$.	AK-47	22-01-14 10:01:59

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Name

Date

[QUE/TH-02001] TH-PROBLEM

Consider a closed cylinder whose walls are adiabatic. The cylinder is divided into three equal parts $A_1$, $A_2$ and $A_3$ by means of partitions $S_1$ and $S_2$, which can move along the length of the cylinder without friction. The partition $S_1$ is adiabatic and $S_2$ is conducting. Initially, each of the three parts contain one mole of Helium gas, which can be treated as an ideal gas, is at pressure $P_0$, temperature $T_0$ and volume $V_0$. Assume the specific heat at constant volume $C_v\,=\,\frac{3R}{2}$ and the specific heat at constant pressure $C_p\,=\,\frac{5R}{2}$. Now, heat is supplied to the to the left most partition $A_1$ till the temperature in part $A_3$ becomes $T_3\,=\,\frac{9T_0}{4}$ Find the final volume, pressure and temperature in terms of $V_0$, $P_0$ and $T_0$. Assume the entire process is quasistatic.
\vskip 3mm
3. ( Continuation of problem 2)

(a) What is work done by the gas in $A_1$ ?

(b) What is the heat supplied to the gas in $A_1$?

AK-47

22-01-14 10:01:44

[QUE/TH-05003] TH-PROBLEM

Consider $n$ mole of ideal gas whose entropy is given by $$ \frac{n}{2}\left[c_1\,+\,5R{\ln}\frac{U}{n}\,+\,2R{\ln}\frac{V}{n} \right]$$ where $R$ is the univeral gas constant, $U$ the internal energy, $V$ the volume and $c_1$ a constant.

Calculate the specific heats $c_V$ and $c_p$
A room is at a temperature $273^o$ K which is in equilbrium with the surroundings. One hour after turning on a heater, the room is at $300^o$ K. Assuming the air is described by the equation given above, find the energy density for the two different temperatures. Answer should be in terms of the atmospheric pressure $P_0$, assume it is constant and the room is always at $P_0$.

AK-47

22-01-14 10:01:59